Problem: The equation of a circle $C$ is $x^2+y^2+10y-11 = 0$. What is its center $(h, k)$ and its radius $r$ ?
Explanation: To find the equation in standard form, complete the square. $(x^2) + (y^2+10y) = 11$ $(x^2) + (y^2+10y+25) = 11 + 0 + 25$ $x^2 + (y+5)^{2} = 36 = 6^2$ Thus, $(h, k) = (0, -5)$ and $r = 6$.